Home
Class 12
MATHS
If in a right-angled triangle A B C ,...

If in a right-angled triangle `A B C ,` the hypotenuse `A B=p` ,then `vec(AB).vec(AC)+ vec(BC). vec(BA)+ vec(CA).vec(CB)` is equal to `2p^2` b. `(p^2)/2` c. `p^2` d. none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE ENGLISH|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

If in a right-angled triangle A B C , the hypotenuse A B=p ,t h e n vec A BdotA C+ vec B Cdot vec B A+ vec C Adot vec C B is equal to 2p^2 b. (p^2)/2 c. p^2 d. none of these

If vec( A) + vec(B) =vec( C ) , and | vec(A)| =2 | vec( B) | and vec( B). vec( C ) = 0 , then

If | vec(a) xx vec(b) | =4 and | vec(a). vec(b) |=2 , then | vec( a) |^(2) | vec( b) | ^(2) is equal to

Prove that vec(a). {(vec(b) + vec(c)) xx (vec(a) + 2vec(b) + 3vec(c))} = [vec(a) vec(b) vec(c)] .

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are vec(a) , vec(b) , vec(c ) and (vec(a) + vec(b) + vec(c ))/(4) respectively, then the position vector of the orthocentre of this triangle is

In triangle ABC (Figure), which of the following is not true: (A) vec(AB)+ vec(BC)+ vec(CA)=vec0 (B) vec(AB)+ vec(BC)- vec(AC) =vec0 (C) vec(AB)+ vec(BC)- vec(CA)=vec0 (D) vec(AB)+ vec(CB)+ vec(CA)=vec0

If a ,\ b ,\ c are non coplanar vectors then ( vec adot( vec bxx vec c))/(( vec cxx vec a)dot vec b)+( vec bdot( vec axx vec c))/( vec cdot( vec axx vec b)) is equal to 2 b. "\ "0"\ " c. 1 d. none of these

In a trapezium ABCD the vector B vec C = alpha vec(AD). If vec p = A vec C + vec(BD) is coillinear with vec(AD) such that vec p = mu vec (AD), then

In a trapezium ABCD the vector B vec C = lambda vec(AD). If vec p = A vec C + vec(BD) is coillinear with vec(AD) such that vec p = mu vec (AD), then

If vec a is parallel to vec bxx vec c , then ( vec axx vec b)dot( vec axx vec c) is equal to | vec a|^2( vec bdot vec c) b. | vec b|^2( vec adot vec c) c. | vec c|^2( vec adot vec b) d. none of these

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j- hat k , vec c= hat...

    Text Solution

    |

  2. Let vec P R=3 hat i+ hat j-2 hat ka n d vec S Q= hat i-3 hat j-4 hat ...

    Text Solution

    |

  3. If in a right-angled triangle A B C , the hypotenuse A B=p ,then ...

    Text Solution

    |

  4. If vec a=( hat i+ hat j+ hat k), vec a. vec b=1a n d vec axx vec b= h...

    Text Solution

    |

  5. If veca satisfies vec axx( hat i+2 hat j+ hat k)= hat i- hat k , then...

    Text Solution

    |

  6. If vec rdot vec a= vec rdot vec b= vec rdot vec c=0,w h e r e vec a ,...

    Text Solution

    |

  7. The unit vector orthogonal to vector -hat i+ hat j+2 hat k and maki...

    Text Solution

    |

  8. Vectors 3 vec a-5 vec b and 2 vec a+ vec b are mutually perpendicular....

    Text Solution

    |

  9. If vectors vec a and vec b are two adjacent sides of a parallelogra...

    Text Solution

    |

  10. The value of x for which the angle between vec a=2x^2 hat i+4x hat ...

    Text Solution

    |

  11. Let vec a* vec b=0,w h e r e vec aa n d vec b are unit vectors and th...

    Text Solution

    |

  12. A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b...

    Text Solution

    |

  13. Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+lam...

    Text Solution

    |

  14. If a \ a n d \ c are unit vectors and |b|=4 . The angel between aa n d...

    Text Solution

    |

  15. If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero ve...

    Text Solution

    |

  16. Let vec a , vec b , a n d vec c be three non-coplanar vectors and ...

    Text Solution

    |

  17. If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec ...

    Text Solution

    |

  18. If vec a \ a n d \ vec b are two non-collinear unit vector, and ...

    Text Solution

    |

  19. The angles of triangle, two of whose sides are represented by vector...

    Text Solution

    |

  20. vec a , vec b ,a n d vec c are unimodular and coplanar. A unit vector...

    Text Solution

    |